Ultimately Constant Abelian Complexity of Infinite Words

It is known that there are recurrent words with constant abelian complexity three, but not with constant complexity four. We prove that there are recurrent words with ultimately constant complexity c for every c.

[1]  J. Allouche.  Algebraic Combinatorics on Words , 2005 .

[2]  Jean-Paul Allouche,et al.  Sur la complexite des suites in nies , 1994 .

[3]  Narad Rampersad,et al.  Recurrent words with constant Abelian complexity , 2009, Adv. Appl. Math..

[4]  Ethan M. Coven,et al.  Sequences with minimal block growth , 2005, Mathematical systems theory.

[5]  Ethan M. Coven,et al.  Sequences with minimal block growth II , 1973, Mathematical systems theory.

[6]  Gwénaël Richomme,et al.  Abelian complexity of minimal subshifts , 2009, J. Lond. Math. Soc..

[7]  Christian Choffrut,et al.  Combinatorics of Words , 1997, Handbook of Formal Languages.